Not an expert, but it's my impression that it's common to have reactors shut down about one month per year for refueling and maintenance. Of course, this can be planned so it's not a big deal.
The plants do have a worse correlated failure mode which is when something bad is discovered in one plant, it can shut down multiple plants because the safety is based on making sure to an extremely high degree that nothing can go wrong - like grounded air planes. Something like Fukushima can shut down plants all over the world temporarily until plans have been revisited and extra precautions possibly put in place.
The plants do have a worse correlated failure mode which is when something bad is discovered in one plant, it can shut down multiple plants because the safety is based on making sure to an extremely high degree that nothing can go wrong - like grounded air planes. Something like Fukushima can shut down plants all over the world temporarily until plans have been revisited and extra precautions possibly put in place.